Sound attenuation in low temperature amorphous solids originates from their disordered structure. However, its detailed mechanism is still being debated. Here we analyze sound attenuation starting directly from the microscopic equations of motion. We
derive an exact expression for the zero-temperature sound damping coefficient and verify that it agrees with results of earlier sound attenuation simulations. The small wavevector analysis of this expression shows that sound attenuation is primarily determined by the non-affine displacements contribution to the wave propagation coefficient coming from the frequency shell of the sound wave.
Glasses possess more low-frequency vibrational modes than predicted by Debye theory. These excess modes are crucial for the understanding the low temperature thermal and mechanical properties of glasses, which differ from those of crystalline solids.
Recent simulational studies suggest that the density of the excess modes scales with their frequency $omega$ as $omega^4$ in two and higher dimensions. Here, we present extensive numerical studies of two-dimensional model glass formers over a large range of glass stabilities. We find that the density of the excess modes follows $D_text{exc}(omega)sim omega^2 $ up to around the boson peak, regardless of the glass stability. The stability dependence of the overall scale of $D_text{exc}(omega)$ correlates with the stability dependence of low-frequency sound attenuation. However, we also find that in small systems, where the first sound mode is pushed to higher frequencies, at frequencies below the first sound mode there are excess modes with a system size independent density of states that scales as $omega^3$.
We derive a distribution function for the position of a tagged active particle in a slowly varying in space external potential, in a system of interacting active particles. The tagged particle distribution has the form of the Boltzmann distribution b
ut with an effective temperature that replaces the temperature of the heat bath. We show that the effective temperature that enters the tagged particle distribution is the same as the effective temperature defined through the Einstein relation, i.e. it is equal to the ratio of the self-diffusion and tagged particle mobility coefficients. This shows that this effective temperature, which is defined through a fluctuation-dissipation ratio, is relevant beyond the linear response regime. We verify our theoretical findings through computer simulations. Our theory fails when an additional large length scale appears in our active system. This length scale is associated with long-wavelength density fluctuations that emerge upon approaching motility-induced phase separation.
Model systems of self-propelled particles reproduce many phenomena observed in laboratory active matter systems that defy our thermal equilibrium-based intuition. In particular, in stationary states of self-propelled systems, it is recognized that ve
locities of different particles exhibit non-trivial equal-time correlations. Such correlations are absent in equivalent equilibrium systems. Recently, researchers found that the range of the velocity correlations increases with increasing persistence time of the self-propulsion and can extend over many particle diameters. Here we review the initial studies of long-ranged velocity correlations in solid-like systems of self-propelled particles. Then, we demonstrate that the long-ranged velocity correlations are also present in dense fluid-like systems. We show that the range of velocity correlations in dense systems of self-propelled particles is determined by the combination of the self-propulsion and the virial bulk modulus that originates from repulsive interparticle interactions.
We recently argued that a self-propelled particle is formally equivalent to a system consisting of two subsystems coupled by a non-reciprocal interaction [Phys. Rev. E 100, 050603(R) (2019)]. Here we show that this non-reciprocal coupling allows to e
xtract useful work from a single self-propelled particle maintained at constant temperature, by using an aligning interaction to influence correlations between the particles position and self-propulsion.
Active matter systems are driven out of equilibrium at the level of individual constituents. One widely studied class are systems of athermal particles that move under the combined influence of interparticle interactions and self-propulsions, with th
e latter evolving according to the Ornstein-Uhlenbeck stochastic process. Intuitively, these so-called active Ornstein-Uhlenbeck particles (AOUPs) systems are farther from equilibrium for longer self-propulsion persistence times. Quantitatively, this is confirmed by the increasing equal-time velocity correlations (which are trivial in equilibrium) and by the increasing violation of the Einstein relation between the self-diffusion and mobility coefficients. In contrast, the entropy production rate, calculated from the ratio of the probabilities of the position space trajectory and its time-reversed counterpart, has a non-monotonic dependence on the persistence time. Thus, it does not properly quantify the departure of AOUPs systems from equilibrium.
The Stokes-Einstein relation (SER) is one of the most robust and widely employed results from the theory of liquids. Yet sizable deviations can be observed for self-solvation, which cannot be explained by the standard hydrodynamic derivation. Here, w
e revisit the work of Masters and Madden [J. Chem. Phys. 74, 2450-2459 (1981)], who first solved a statistical mechanics model of the SER using the projection operator formalism. By generalizing their analysis to all spatial dimensions and to partially structured solvents, we identify a potential microscopic origin of some of these deviations. We also reproduce the SER-like result from the exact dynamics of infinite-dimensional fluids.
Dense assemblies of self-propelled particles undergo a nonequilibrium form of glassy dynamics. Physical intuition suggests that increasing departure from equilibrium due to active forces fluidifies a glassy system. We falsify this belief by devising
a model of self-propelled particles where increasing departure from equilibrium can both enhance or depress glassy dynamics, depending on the chosen state point. We analyze a number of static and dynamic observables and suggest that the location of the nonequilibrium glass transition is primarily controlled by the evolution of two-point static density correlations due to active forces. The dependence of the density correlations on the active forces varies non-trivially with the details of the system, and is difficult to predict theoretically. Our results emphasize the need to develop an accurate liquid state theory for nonequilibrium systems.
We use computer simulations to study the cooling rate dependence of the stability and energetics of model glasses created at constant pressure conditions and compare the results with glasses formed at constant volume conditions. To examine the stabil
ity, we determine the time it takes for a glass cooled and reheated at constant pressure to transform back into a liquid, $t_{mathrm{trans}}$, and calculate the stability ratio $S = t_{mathrm{trans}}/tau_alpha$, where $tau_alpha$ is the equilibrium relaxation time of the liquid. We find that, for slow enough cooling rates, cooling and reheating at constant pressure results in a larger stability ratio $S$ than for cooling and reheating at constant volume. We also compare the energetics of glasses obtained by cooling while maintaining constant pressure with those of glasses created by cooling from the same state point while maintaining constant volume. We find that cooling at constant pressure results in glasses with lower average potential energy and average inherent structure energy. We note that in model simulations of the vapor deposition process glasses are created under constant pressure conditions, and thus they should be compared to glasses obtained by constant pressure cooling.
We study the glassy dynamics taking place in dense assemblies of athermal active particles that are driven solely by a nonequilibrium self-propulsion mechanism. Active forces are modeled as an Ornstein-Uhlenbeck stochastic process, characterized by a
persistence time and an effective temperature, and particles interact via a Lennard-Jones potential that yields well-studied glassy behavior in the Brownian limit, obtained as the persistence time vanishes. By increasing the persistence time, the system departs more strongly from thermal equilibrium and we provide a comprehensive numerical analysis of the structure and dynamics of the resulting active fluid. Finite persistence times profoundly affect the static structure of the fluid and give rise to nonequilibrium velocity correlations that are absent in thermal systems. Despite these nonequilibrium features, for any value of the persistence time we observe a nonequilibrium glass transition as the effective temperature is decreased. Surprisingly, increasing departure from thermal equilibrium is found to promote (rather than suppress) the glassy dynamics. Overall, our results suggest that with increasing persistence time, microscopic properties of the active fluid change quantitatively, but the broad features of the nonequilibrium glassy dynamics observed with decreasing the effective temperature remain qualitatively similar to those of thermal glass-formers.
